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Question 1019896: Consider the function:
f(x)=x^2+4
a Will f(x) +4 have real zeros? Justify without any calculations.
b Will f(x) -5 have real zeros? Justify without any calculations.
c Will f(x-2) have real zeros? Justify without any calculations.
d Will f(x+4) have real zeros? Justify without any calculations.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! a. No. When x=0, x^2 is the smallest it can be. This is not clear, f(x)=4? If it is f(x)+4, the answer is still no.
b. Not clear, but if if it is f(x)-5, then it will have zeros at -1 and 1, because when x=0, f(x) is -1, and when x is greater than 1, the function is positive. Therefore, it has to cross the x-axis
c. f(x-2) All this does is shift the graph to the right.
d. f(x+4). This shifts the graph to the left, and it will not have zeros.
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